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math.NA2026
Structure-Preserving Dynamic Mode Decomposition for Highly Oscillatory Dynamics of Semiclassical Schrödinger Equations
Yizhe Feng, Weiguo Gao, Jia Yin
We propose two novel data-driven dynamic mode decomposition (DMD)-type methods, the Crank--Nicolson DMD and the semi-implicit DMD, to predict the highly oscillatory dynamics of the…
math.NA2026
A sixth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
Weiguo Gao, Zhansi He, Jia Yin
In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as , for solving the Dirac equation in the absence of external magnetic potenti…